Question: Multiply. $977.4 \times 0.3=$
Answer: $9{,}774 \times 3$ and $977.4\times 0.3$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $9{,}774 \times 3$. Then we can estimate to place the decimal point in the product of $977.4 \times 0.3$. $\begin{aligned} {9}{,}774&\\ \underline{ \times {3}}&\\ {12}& {3} \times {4\text{ ones}}\\ {210}& {3} \times {7\text{ tens}}\\ {2{,}100}& {3} \times {7\text{ hundreds}}\\ \underline{+{27{,}000}}& {3} \times {9\text{ thousands}}\\ \end{aligned}$ $\begin{aligned} 9{,}774&\\ \underline{ \times 3}&\\ 12}& {3} \times {4\text{ ones}}\\ 210}& {3} \times {7\text{ tens}}\\ 2{,}100}& {3} \times {7\text{ hundreds}}\\ \underline{+27{,}000}} & {3} \times {9\text{ thousands}}\\ 29{,}322 \end{aligned}$ $9{,}774 \times 3 = 29{,}322$ Let's estimate to place the decimal in $977.4 \times 0.3$. $\begin{aligned} 977.4 \times 0.3 &\approx 1{,}000\times 0.1\\\\ &\approx 100 \end{aligned}$ Where can we place the decimal in $29{,}322$ to get a product close to $100$ ? $977.4\times0.3=293.22$